1. The Trainwreck (similar to win by feeding)

The Trainwreck Approach is where you attempt to create a snowball for your team by initially feinting troll. You give up one kill in the hopes of getting 1 or more in return and putting the enemy out of lane for the first few levels (which is very critical and can even lead to an all mid strategy for an early tower). You barrel out of your base down mid lane and feed them a kill.
You then tell them in all chat that you are going to feed more kills, just be sure to come to the dragon pit for their prize
(you guessed it, coordinate a 5 man gank in river)
Use at your own risk, works moderately well in low elo. Best to try in normals first with an all mid lane strategy.

The trainwreck is not limited to proxy singed, but is probably the most useful when he is on that champion. Other notables trainwreck champion favorites: tryndamere, teemo, master yi, fiora, nidalee and jayce.

2. The Overwarding-Safe Guy

The overwarding-safe guy is usually a support, but is not limited to that role alone. The overwarding-safe guy, could be any role, but is most common on support mains. The overwarding safe guy knows the importance of a ward and he means business. If top lane dies 1v1 and the enemy jungler is at mid, then "top should've had a ward."
Nevermind the fact that it was a 1v1, the overwarding-safe guy knows that wards win games (as we just established).
Some quotes from the overwarding-safe guy:
"Don't worry guy's we got this"

"I'm buying wards for you top lane! I'll brt! I noticed you don't have any either mid, so I'll drop one for you too!"

"Hey Janna, do I need to buy a pink or two for lane? How about a green ward?"

"Hey guys do you think you could come mid and help me push down tower? I have each side bush warded and I think we can make a play."

3. The Delusionist

The Delusionist knows that he is the best member on his team and he must remind himself of that at all points in order to play to the best of his ability. Cognitive dissonance and flaming are a sure bet that you are dealing with this majestic creature. Having a delusionist on your team can actually be beneficial because at the very least, he believes in himself and you absolutely need to in this game. On the other hand, this guy is probably going to lose you the game with his negative attitude and warped view of the metagame.
The Delusionist is not exclusive to mean players, but mean players are predisposed to this type of behavior. :ome quotes from a mad delusionist"

"Omg, why is there always 3 people mid? Can't you guys call mia?"

"Well **** guys, you all fed like hell, but I will carry you."

"That guy just killed me, but he's totally not even good, he just got lucky."

"Don't worry guys, I'm probably going to carry this next teamfight" (Even though they lost the last 8 teamfights and he's hit no on surrender probably 5 times).

4. The Defeatist

The Defeatist Attitude is much more a side effect of ranked than it is a way to approach ranked. Still I figured it was worth a mention because so many people tend to pick this approach (it's the most popular, imo)
Here's a little piece about why:

The Defeatist is unhappy. He is unhappy because of his team's poor performance every game. Not only does he bring the weight of his last loss with him, he also carries the losses of everyone else on his team from that game. He dumped on team morale subtlely all game long and by the time it got to mid game, noone made calls and got flustered from his negative attitude. Despite making big mistakes every game and being overcritical of other's mistakes, the defeatist does not improve, nor does he choose to see his mistakes at all.
This is the type of player you should minimize interaction with and hope that you can carry for long enough so that he shuts up about how bad his team is. Here are some quotes from The Defeatist:

"Omg caitlyn, how are you so ****ING bad? You're seriously losing lane to an Ezreal? What a nub, you should've let me ad."

"GG, this top lane is probably 15. ****ing kids, man, **** this game."

"You know Anivia beats the **** out of ryze right? How could you possibly lose that lane. You must be so ****ing bad at this game!"

"Well we are down 10k gold or more by now. Just surrender" (even though you have a better late game).

p.s. The Defeatist can tell you how much gold the enemy ad has on hand. He can tell you what gank route is optimal for lee sin jungle on purple side. He can even tell you most of the popular counterpicks for mid lane champions, but what he can't do is accept the blame for his losses. When you see a defeatist, swallow your pride, and be ready to mute that person.

5. The Hard Carry

The Hard Carry plays the strongest champions in the game. He knows what's strong, why it's strong, why it's weak against X composition, when to pick it and how to play it in every situation. He rarely gives up deaths and is more likely to win you the game than lose lane. He knows he is a good player, but doesn't let it go to his head. The Hard Carry is a class act. Be aware of his strengths, but don't let that stop you from seeing mistakes. Help the Hard Carry by feeding him usable information at every turn. (Dragon warded, zilean no ult, bot flashes down, etc) It can and will make the difference in your games. When you see a Hard Carry personality, you cling to his coattails and never let go.
Some quotes from the hard carry:

"D1 smurf, don't feed."

"I've probably played this matchup more times than I can count."

"Lol, that guy didn't even see it coming."

"Top lane, please buy a ward. If you need ganks, how am I supposed to help you without vision?"

BONUS

The All Chat

The All Chat approach is something that I've used quite extensively in my past. You don't always talk in all chat, but when you do, it's to gloat to the person you just killed. I am far from abusing this strategy at my current iteration, but there was a time when I thought it was simply hilarious to start a fight on the enemy team and make a free win out of it.

So that's what I did. The All Chat Approach is practically a guaranteed win if you time it right. Noone is going to go on tilt because you kill someone once, it's the games where you are one or two kills up on your enemies and they have a good shot to win where you want to use this tactic. If you say "lol, EZ" after killing someone for the second time, that will most likely send a red flag to the enemy team and they will most likely flame that guy to all hell.

With any luck, that will delay him from getting back to lane and probably make him play worse as a direct result. The All Chat Approach isn't something that is particularly reliable, but it can be pretty useful in close games sometimes. All it takes is one mistake from someone that is already in bad standing with another player for them to "afk."

So, you don't talk **** unnecessarily (it will make you look like a complete douche), you just highlight losing lanes on the enemy team and make them feel dominated. Be wary of counterganks and extra attention from this strategy. The All Chat Approach works best when you play an annoying hero like Teemo that wants to draw people to his lane, as that is part of his champion design.
Here are some quotes from The All Chat Approach:

"LOL wtf was that? Dat flash."

"Jarvan 0-3 and only 28 cs? ROFL"

"So, how does your mid fall behind by 50 cs in 10 minutes? Just wondering."

"Hey guys, I'm about to dance at your blue buff, meet me there for a good time."